Matlis reflexive and generalized local cohomology modules

Mafi, Amir

Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 1095-1102.

Résumé

Let $(R,\mathfrak m )$ be a complete local ring, $\mathfrak a $ an ideal of $R$ and $N$ and $L$ two Matlis reflexive $R$-modules with $\mathop{{\rm Supp}} (L)\subseteq V(\mathfrak a )$. We prove that if $M$ is a finitely generated $R$-module, then $\mathop{{\rm Ext}}\nolimits_R^i(L,H_{\mathfrak a }^j(M,N))$ is Matlis reflexive for all $i$ and $j$ in the following cases: (a) $\mathop{{\rm dim}} R/{\mathfrak a }=1$; (b) $\mathop{{\rm cd}} (\mathfrak a )=1$; where $\mathop{{\rm cd}} $ is the cohomological dimension of $\mathfrak a $ in $R$; (c) $\mathop{{\rm dim}} R\leq 2$. In these cases we also prove that the Bass numbers of $H_{\mathfrak a }^j(M,N)$ are finite.

Détail

Classification : 13D07, 13D45, 13E99
Keywords: Bass numbers; generalized local cohomology modules; Matlis reflexive